POJ 2352 Stars

最新推荐文章于 2021-05-03 20:08:45 发布

ChiLuManXi

最新推荐文章于 2021-05-03 20:08:45 发布

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本文链接：https://blog.youkuaiyun.com/ChiLuManXi/article/details/50620210

本文介绍了一道关于星图中星星等级统计的算法题，通过树状数组的数据结构实现对星星等级的有效计算。文章提供了完整的代码示例及解析。

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Stars

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 39399		Accepted: 17110

Description

Astronomers often examine star maps where stars are represented by points on a plane and each star has Cartesian coordinates. Let the level of a star be an amount of the stars that are not higher and not to the right of the given star. Astronomers want to know the distribution of the levels of the stars.

For example, look at the map shown on the figure above. Level of the star number 5 is equal to 3 (it's formed by three stars with a numbers 1, 2 and 4). And the levels of the stars numbered by 2 and 4 are 1. At this map there are only one star of the level 0, two stars of the level 1, one star of the level 2, and one star of the level 3.

You are to write a program that will count the amounts of the stars of each level on a given map.

Input

The first line of the input file contains a number of stars N (1<=N<=15000). The following N lines describe coordinates of stars (two integers X and Y per line separated by a space, 0<=X,Y<=32000). There can be only one star at one point of the plane. Stars are listed in ascending order of Y coordinate. Stars with equal Y coordinates are listed in ascending order of X coordinate.

Output

The output should contain N lines, one number per line. The first line contains amount of stars of the level 0, the second does amount of stars of the level 1 and so on, the last line contains amount of stars of the level N-1.

Sample Input

Sample Output

Hint

This problem has huge input data,use scanf() instead of cin to read data to avoid time limit exceed.

题意是给定一系列的坐标，每个坐标代表一个点，点x满足横坐标和纵坐标均小于点y的话，x等级可以加1，求解从等级0到等级n - 1的星的个数。

树状数组基础题，求解方法是多维护一个数组，下标代表等级，用树状数组的性质，其下标来存储每个星星的等级，因为题目给出，恰好是按照y递增的顺序，所以可以每次添加一个星星的时候，更新树状数组，并计算该星星等级使维护等级的数组对应单元加1.最后遍历输出即可，代码如下：

/*************************************************************************
	> File Name: Stars.cpp
	> Author: Zhanghaoran
	> Mail: chilumanxi@xiyoulinux.org
	> Created Time: 2016年01月30日 星期六 18时11分24秒
 ************************************************************************/

#include <iostream>
#include <algorithm>
#include <cstring>
#include <cstdio>
#include <cstdlib>

using namespace std;

const int Max = 32010;
int n;
int tree[Max];
int ans[Max];

int check(int x){
    int sum = 0;
    while(x){
        sum += tree[x];
        x -= x & -x;
    }
    return sum;
}

void add(int x){
    while(x < Max){
        tree[x] ++;
        x += x & -x;
    }
}

int main(void){
    scanf("%d", &n);
    int x, y;
    for(int i = 0; i < n; i ++){
        scanf("%d %d", &x, &y);
        ++ x;
        ++ ans[check(x)];
        add(x);
    }

    for(int i = 0; i < n; i ++){
        printf("%d\n", ans[i]);
    }
    return 0;

}

查看原文：http://chilumanxi.org/2016/02/01/poj-2352-stars/